The North African team, who defeated Spain on penalties in the round of 16, will play Portugal at Al Thumama Stadium in Qatar as the fourth African nation, following Cameroon, Senegal and Ghana, to ever reach the quarterfinals of the tournament.
A World Cup semifinal against either England or France is up for grabs, alongside a place in the history books.
Cameroon in 1990, Senegal's 2002 side and the 2010 Ghana team all fell at the quarterfinal stage.
"We have nothing to lose. The challenge is to do as well as we did in the previous games," Regragui said on the eve of the match against Portugal.
"We want to show that Africa deserves to be here, Morocco deserves to be here...We have a whole people behind us, a continent behind us and the Arab world behind us," Regragui added.
Morocco has the best defensive record in the tournament, having conceded only one goal in their four matches.
But Regragui warned: "We can't rest on our laurels. We haven't got carried away, we've just surprised a few people and a few algorithms who expected Belgium or Spain to be in the quarter-finals."
Morocco's success in Qatar has sparked celebrations back home, but also in several European countries where the Moroccan diaspora live.
Fourteen of Regragui's 26-man squad were born outside the African country.
"People are identifying with us and we've managed to unite Moroccans behind this football team," he said. "I think that's worth more than anything, it's worth more than money, it's worth more than titles.
"We've made people happy, we've made people proud but that's not the only reason we're here — we're here to win matches and go as far as we can in this tournament."
The Lions of Atlas have had a series of injury concerns, with full-backs Achraf Hakimi and Noussair Mazraoui playing despite not being fully fit.
Center-back Nayef Aguerd hobbled off injured in the Spain match but could be ready to play on Saturday.
"Lots of injuries, people sick. We've played lots of games without people 100%," Regragui said.
"I'm proud for that because nobody has seen Morocco at 100% power. Aguerd is waiting tomorrow to see if he can play or not."